The question of the actual pronunciation of both monsieur and monseigneur need not be asked, but I will try and answer the other part of the question, i.e. why is the combination of the letters (o+n) pronounced differently in each word.
I'll start by quoting David Crystal "Languages are always in a state of flux... the most noticeable and frequent changes affect pronunciation and vocabulary...".
Vowel sounds are more prone to evolution than consonants. I suppose it is because phonatory organs are not as easily controlled when sounding vowels than when sounding consonants (just a hint, but the question could be asked on linguistics Stack Exchange1.
Another factor in pronunciation evolution is the question of the stressed syllables. Vowels will change more easily when unstressed.
Now, back to monsieur and monseigneur. Both are a combination of the possessive mon + sieur or seigneur, and both were written as two separate words that concatenated as the French language evolved.
When said as two separate words (mon+sieur), had two equally stressed syllables. But as the words evolved into one single entity with a shift in meaning and the loss of the understanding of the original meaning (including the fact that mon was no longer perceived as a possessive) the first syllable became unstressed (French words are regularly stressed on the last syllable), the nasal /ɔ̃/ evolved into the unstressed vowel sound /ə/.
In monseigneur, even when concatenated into one single word the mon has always retained its possessive meaning (I suppose we could say that French people still perceive the word monseigneur as the English perceive my lord), and even nowadays when we say the word we tend to have an auxiliary stress on the first syllable, thus the original /ɔ̃/ sound remaining unchanged.
For more on the evolution of vowel pronunciation in the French language one could have a look at the wikipedia article on Old French and at this book: Introduction à la phonétique historique du français
by Annick Englebert for a study of the historical evolution of French pronunciation.
1 I asked the question on Linguistics and got very interesting answers.